How do I apply different normal maps in different areas inside a material?
You'll need to do three things :).
1. Create a separate UV map for each texture (3 in total).
Only faces you put inside UV bounds will be used. Faces outside bounds will be ignored.

2. Connect a different UV map to each texture (use the UV Map node).
Set textures to Clip, so they don't repeat.
3. Combine the textures using Mix RGB nodes set to Add, fac=1.
And plug the result into a Normal Map node.